/**
 * @license Highcharts JS v8.0.0 (2019-12-10)
 *
 * (c) 2017-2019 Highsoft AS
 * Authors: Jon Arild Nygard
 *
 * License: www.highcharts.com/license
 */
"use strict";
(function (factory) {
  if (typeof module === "object" && module.exports) {
    factory["default"] = factory;
    module.exports = factory;
  } else if (typeof define === "function" && define.amd) {
    define("highcharts/modules/venn", ["highcharts"], function (Highcharts) {
      factory(Highcharts);
      factory.Highcharts = Highcharts;
      return factory;
    });
  } else {
    factory(typeof Highcharts !== "undefined" ? Highcharts : undefined);
  }
})(function (Highcharts) {
  var _modules = Highcharts ? Highcharts._modules : {};
  function _registerModule(obj, path, args, fn) {
    if (!obj.hasOwnProperty(path)) {
      obj[path] = fn.apply(null, args);
    }
  }
  _registerModule(_modules, "mixins/draw-point.js", [], function () {
    /* *
     *
     *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
     *
     * */
    var isFn = function (x) {
      return typeof x === "function";
    };
    /* eslint-disable no-invalid-this, valid-jsdoc */
    /**
     * Handles the drawing of a component.
     * Can be used for any type of component that reserves the graphic property, and
     * provides a shouldDraw on its context.
     *
     * @private
     * @function draw
     * @param {DrawPointParams} params
     *        Parameters.
     *
     * @todo add type checking.
     * @todo export this function to enable usage
     */
    var draw = function draw(params) {
      var component = this,
        graphic = component.graphic,
        animatableAttribs = params.animatableAttribs,
        onComplete = params.onComplete,
        css = params.css,
        renderer = params.renderer;
      if (component.shouldDraw()) {
        if (!graphic) {
          component.graphic = graphic = renderer[params.shapeType](
            params.shapeArgs
          ).add(params.group);
        }
        graphic
          .css(css)
          .attr(params.attribs)
          .animate(
            animatableAttribs,
            params.isNew ? false : void 0,
            onComplete
          );
      } else if (graphic) {
        var destroy = function () {
          component.graphic = graphic = graphic.destroy();
          if (isFn(onComplete)) {
            onComplete();
          }
        };
        // animate only runs complete callback if something was animated.
        if (Object.keys(animatableAttribs).length) {
          graphic.animate(animatableAttribs, void 0, function () {
            destroy();
          });
        } else {
          destroy();
        }
      }
    };
    /**
     * An extended version of draw customized for points.
     * It calls additional methods that is expected when rendering a point.
     * @private
     * @param {Highcharts.Dictionary<any>} params Parameters
     */
    var drawPoint = function drawPoint(params) {
      var point = this,
        attribs = (params.attribs = params.attribs || {});
      // Assigning class in dot notation does go well in IE8
      // eslint-disable-next-line dot-notation
      attribs["class"] = point.getClassName();
      // Call draw to render component
      draw.call(point, params);
    };

    return drawPoint;
  });
  _registerModule(_modules, "mixins/geometry.js", [], function () {
    /* *
     *
     *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
     *
     * */
    /**
     * Calculates the center between a list of points.
     * @private
     * @param {Array<Highcharts.PositionObject>} points
     *        A list of points to calculate the center of.
     * @return {Highcharts.PositionObject}
     *         Calculated center
     */
    var getCenterOfPoints = function getCenterOfPoints(points) {
      var sum = points.reduce(
        function (sum, point) {
          sum.x += point.x;
          sum.y += point.y;
          return sum;
        },
        { x: 0, y: 0 }
      );
      return {
        x: sum.x / points.length,
        y: sum.y / points.length,
      };
    };
    /**
     * Calculates the distance between two points based on their x and y
     * coordinates.
     * @private
     * @param {Highcharts.PositionObject} p1
     *        The x and y coordinates of the first point.
     * @param {Highcharts.PositionObject} p2
     *        The x and y coordinates of the second point.
     * @return {number}
     *         Returns the distance between the points.
     */
    var getDistanceBetweenPoints = function getDistanceBetweenPoints(p1, p2) {
      return Math.sqrt(Math.pow(p2.x - p1.x, 2) + Math.pow(p2.y - p1.y, 2));
    };
    /**
     * Calculates the angle between two points.
     * @todo add unit tests.
     * @private
     * @param {Highcharts.PositionObject} p1 The first point.
     * @param {Highcharts.PositionObject} p2 The second point.
     * @return {number} Returns the angle in radians.
     */
    var getAngleBetweenPoints = function getAngleBetweenPoints(p1, p2) {
      return Math.atan2(p2.x - p1.x, p2.y - p1.y);
    };
    var geometry = {
      getAngleBetweenPoints: getAngleBetweenPoints,
      getCenterOfPoints: getCenterOfPoints,
      getDistanceBetweenPoints: getDistanceBetweenPoints,
    };

    return geometry;
  });
  _registerModule(
    _modules,
    "mixins/geometry-circles.js",
    [_modules["mixins/geometry.js"]],
    function (geometry) {
      /* *
       *
       *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
       *
       * */
      var getAngleBetweenPoints = geometry.getAngleBetweenPoints,
        getCenterOfPoints = geometry.getCenterOfPoints,
        getDistanceBetweenPoints = geometry.getDistanceBetweenPoints;
      /**
       * @private
       * @param {number} x
       *        Number to round
       * @param {number} decimals
       *        Number of decimals to round to
       * @return {number}
       *         Rounded number
       */
      function round(x, decimals) {
        var a = Math.pow(10, decimals);
        return Math.round(x * a) / a;
      }
      /**
       * Calculates the area of a circle based on its radius.
       * @private
       * @param {number} r
       *        The radius of the circle.
       * @return {number}
       *         Returns the area of the circle.
       */
      function getAreaOfCircle(r) {
        if (r <= 0) {
          throw new Error("radius of circle must be a positive number.");
        }
        return Math.PI * r * r;
      }
      /**
       * Calculates the area of a circular segment based on the radius of the circle
       * and the height of the segment.
       * See http://mathworld.wolfram.com/CircularSegment.html
       * @private
       * @param {number} r
       *        The radius of the circle.
       * @param {number} h
       *        The height of the circular segment.
       * @return {number}
       *         Returns the area of the circular segment.
       */
      function getCircularSegmentArea(r, h) {
        return (
          r * r * Math.acos(1 - h / r) - (r - h) * Math.sqrt(h * (2 * r - h))
        );
      }
      /**
       * Calculates the area of overlap between two circles based on their radiuses
       * and the distance between them.
       * See http://mathworld.wolfram.com/Circle-CircleIntersection.html
       * @private
       * @param {number} r1
       *        Radius of the first circle.
       * @param {number} r2
       *        Radius of the second circle.
       * @param {number} d
       *        The distance between the two circles.
       * @return {number}
       *         Returns the area of overlap between the two circles.
       */
      function getOverlapBetweenCircles(r1, r2, d) {
        var overlap = 0;
        // If the distance is larger than the sum of the radiuses then the circles
        // does not overlap.
        if (d < r1 + r2) {
          if (d <= Math.abs(r2 - r1)) {
            // If the circles are completely overlapping, then the overlap
            // equals the area of the smallest circle.
            overlap = getAreaOfCircle(r1 < r2 ? r1 : r2);
          } else {
            // Height of first triangle segment.
            var d1 = (r1 * r1 - r2 * r2 + d * d) / (2 * d),
              // Height of second triangle segment.
              d2 = d - d1;
            overlap =
              getCircularSegmentArea(r1, r1 - d1) +
              getCircularSegmentArea(r2, r2 - d2);
          }
          // Round the result to two decimals.
          overlap = round(overlap, 14);
        }
        return overlap;
      }
      /**
       * Calculates the intersection points of two circles.
       *
       * NOTE: does not handle floating errors well.
       * @private
       * @param {Highcharts.CircleObject} c1
       *        The first circle.
       * @param {Highcharts.CircleObject} c2
       *        The second sircle.
       * @return {Array<Highcharts.PositionObject>}
       *         Returns the resulting intersection points.
       */
      function getCircleCircleIntersection(c1, c2) {
        var d = getDistanceBetweenPoints(c1, c2),
          r1 = c1.r,
          r2 = c2.r;
        var points = [];
        if (d < r1 + r2 && d > Math.abs(r1 - r2)) {
          // If the circles are overlapping, but not completely overlapping, then
          // it exists intersecting points.
          var r1Square = r1 * r1,
            r2Square = r2 * r2,
            // d^2 - r^2 + R^2 / 2d
            x = (r1Square - r2Square + d * d) / (2 * d),
            // y^2 = R^2 - x^2
            y = Math.sqrt(r1Square - x * x),
            x1 = c1.x,
            x2 = c2.x,
            y1 = c1.y,
            y2 = c2.y,
            x0 = x1 + (x * (x2 - x1)) / d,
            y0 = y1 + (x * (y2 - y1)) / d,
            rx = -(y2 - y1) * (y / d),
            ry = -(x2 - x1) * (y / d);
          points = [
            { x: round(x0 + rx, 14), y: round(y0 - ry, 14) },
            { x: round(x0 - rx, 14), y: round(y0 + ry, 14) },
          ];
        }
        return points;
      }
      /**
       * Calculates all the intersection points for between a list of circles.
       * @private
       * @param {Array<Highcharts.CircleObject>} circles
       *        The circles to calculate the points from.
       * @return {Array<Highcharts.GeometryObject>}
       *         Returns a list of intersection points.
       */
      function getCirclesIntersectionPoints(circles) {
        return circles.reduce(function (points, c1, i, arr) {
          var additional = arr.slice(i + 1).reduce(function (points, c2, j) {
            var indexes = [i, j + i + 1];
            return points.concat(
              getCircleCircleIntersection(c1, c2).map(function (p) {
                p.indexes = indexes;
                return p;
              })
            );
          }, []);
          return points.concat(additional);
        }, []);
      }
      /**
       * Tests wether the first circle is completely overlapping the second circle.
       *
       * @private
       * @param {Highcharts.CircleObject} circle1 The first circle.
       * @param {Highcharts.CircleObject} circle2 The The second circle.
       * @return {boolean} Returns true if circle1 is completely overlapping circle2,
       * false if not.
       */
      function isCircle1CompletelyOverlappingCircle2(circle1, circle2) {
        return (
          getDistanceBetweenPoints(circle1, circle2) + circle2.r <
          circle1.r + 1e-10
        );
      }
      /**
       * Tests wether a point lies within a given circle.
       * @private
       * @param {Highcharts.PositionObject} point
       *        The point to test for.
       * @param {Highcharts.CircleObject} circle
       *        The circle to test if the point is within.
       * @return {boolean}
       *         Returns true if the point is inside, false if outside.
       */
      function isPointInsideCircle(point, circle) {
        return getDistanceBetweenPoints(point, circle) <= circle.r + 1e-10;
      }
      /**
       * Tests wether a point lies within a set of circles.
       * @private
       * @param {Highcharts.PositionObject} point
       *        The point to test.
       * @param {Array<Highcharts.CircleObject>} circles
       *        The list of circles to test against.
       * @return {boolean}
       *         Returns true if the point is inside all the circles, false if not.
       */
      function isPointInsideAllCircles(point, circles) {
        return !circles.some(function (circle) {
          return !isPointInsideCircle(point, circle);
        });
      }
      /**
       * Tests wether a point lies outside a set of circles.
       *
       * TODO: add unit tests.
       * @private
       * @param {Highcharts.PositionObject} point
       *        The point to test.
       * @param {Array<Highcharts.CircleObject>} circles
       *        The list of circles to test against.
       * @return {boolean}
       *         Returns true if the point is outside all the circles, false if not.
       */
      function isPointOutsideAllCircles(point, circles) {
        return !circles.some(function (circle) {
          return isPointInsideCircle(point, circle);
        });
      }
      /**
       * Calculates the points for the polygon of the intersection area between a set
       * of circles.
       *
       * @private
       * @param {Array<Highcharts.CircleObject>} circles
       *        List of circles to calculate polygon of.
       * @return {Array<Highcharts.GeometryObject>} Return list of points in the
       * intersection polygon.
       */
      function getCirclesIntersectionPolygon(circles) {
        return getCirclesIntersectionPoints(circles).filter(function (p) {
          return isPointInsideAllCircles(p, circles);
        });
      }
      /**
       * Calculate the path for the area of overlap between a set of circles.
       * @todo handle cases with only 1 or 0 arcs.
       * @private
       * @param {Array<Highcharts.CircleObject>} circles
       *        List of circles to calculate area of.
       * @return {Highcharts.GeometryIntersectionObject|undefined}
       *         Returns the path for the area of overlap. Returns an empty string if
       *         there are no intersection between all the circles.
       */
      function getAreaOfIntersectionBetweenCircles(circles) {
        var intersectionPoints = getCirclesIntersectionPolygon(circles),
          result;
        if (intersectionPoints.length > 1) {
          // Calculate the center of the intersection points.
          var center_1 = getCenterOfPoints(intersectionPoints);
          intersectionPoints = intersectionPoints
            // Calculate the angle between the center and the points.
            .map(function (p) {
              p.angle = getAngleBetweenPoints(center_1, p);
              return p;
            })
            // Sort the points by the angle to the center.
            .sort(function (a, b) {
              return b.angle - a.angle;
            });
          var startPoint = intersectionPoints[intersectionPoints.length - 1];
          var arcs = intersectionPoints.reduce(
            function (data, p1) {
              var startPoint = data.startPoint,
                midPoint = getCenterOfPoints([startPoint, p1]);
              // Calculate the arc from the intersection points and their
              // circles.
              var arc = p1.indexes
                // Filter out circles that are not included in both
                // intersection points.
                .filter(function (index) {
                  return startPoint.indexes.indexOf(index) > -1;
                })
                // Iterate the circles of the intersection points and
                // calculate arcs.
                .reduce(function (arc, index) {
                  var circle = circles[index],
                    angle1 = getAngleBetweenPoints(circle, p1),
                    angle2 = getAngleBetweenPoints(circle, startPoint),
                    angleDiff =
                      angle2 - angle1 + (angle2 < angle1 ? 2 * Math.PI : 0),
                    angle = angle2 - angleDiff / 2;
                  var width = getDistanceBetweenPoints(midPoint, {
                    x: circle.x + circle.r * Math.sin(angle),
                    y: circle.y + circle.r * Math.cos(angle),
                  });
                  var r = circle.r;
                  // Width can sometimes become to large due to floating
                  // point errors
                  if (width > r * 2) {
                    width = r * 2;
                  }
                  // Get the arc with the smallest width.
                  if (!arc || arc.width > width) {
                    arc = {
                      r: r,
                      largeArc: width > r ? 1 : 0,
                      width: width,
                      x: p1.x,
                      y: p1.y,
                    };
                  }
                  // Return the chosen arc.
                  return arc;
                }, null);
              // If we find an arc then add it to the list and update p2.
              if (arc) {
                var r = arc.r;
                data.arcs.push(["A", r, r, 0, arc.largeArc, 1, arc.x, arc.y]);
                data.startPoint = p1;
              }
              return data;
            },
            {
              startPoint: startPoint,
              arcs: [],
            }
          ).arcs;
          if (arcs.length === 0) {
            // empty
          } else if (arcs.length === 1) {
            // empty
          } else {
            arcs.unshift(["M", startPoint.x, startPoint.y]);
            result = {
              center: center_1,
              d: arcs,
            };
          }
        }
        return result;
      }
      var geometryCircles = {
        getAreaOfCircle: getAreaOfCircle,
        getAreaOfIntersectionBetweenCircles:
          getAreaOfIntersectionBetweenCircles,
        getCircleCircleIntersection: getCircleCircleIntersection,
        getCirclesIntersectionPoints: getCirclesIntersectionPoints,
        getCirclesIntersectionPolygon: getCirclesIntersectionPolygon,
        getCircularSegmentArea: getCircularSegmentArea,
        getOverlapBetweenCircles: getOverlapBetweenCircles,
        isCircle1CompletelyOverlappingCircle2:
          isCircle1CompletelyOverlappingCircle2,
        isPointInsideCircle: isPointInsideCircle,
        isPointInsideAllCircles: isPointInsideAllCircles,
        isPointOutsideAllCircles: isPointOutsideAllCircles,
        round: round,
      };

      return geometryCircles;
    }
  );
  _registerModule(_modules, "mixins/nelder-mead.js", [], function () {
    /* *
     *
     *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
     *
     * */
    /* eslint-disable valid-jsdoc */
    var getCentroid = function (simplex) {
      var arr = simplex.slice(0, -1),
        length = arr.length,
        result = [],
        sum = function (data, point) {
          data.sum += point[data.i];
          return data;
        };
      for (var i = 0; i < length; i++) {
        result[i] = arr.reduce(sum, { sum: 0, i: i }).sum / length;
      }
      return result;
    };
    /**
     * Finds an optimal position for a given point.
     * @todo add unit tests.
     * @todo add constraints to optimize the algorithm.
     * @private
     * @param {Highcharts.NelderMeadTestFunction} fn
     *        The function to test a point.
     * @param {Highcharts.NelderMeadPointArray} initial
     *        The initial point to optimize.
     * @return {Highcharts.NelderMeadPointArray}
     *         Returns the opimized position of a point.
     */
    var nelderMead = function nelderMead(fn, initial) {
      var maxIterations = 100,
        sortByFx = function (a, b) {
          return a.fx - b.fx;
        },
        pRef = 1, // Reflection parameter
        pExp = 2, // Expansion parameter
        pCon = -0.5, // Contraction parameter
        pOCon = pCon * pRef, // Outwards contraction parameter
        pShrink = 0.5; // Shrink parameter
      /**
       * @private
       */
      var weightedSum = function weightedSum(weight1, v1, weight2, v2) {
        return v1.map(function (x, i) {
          return weight1 * x + weight2 * v2[i];
        });
      };
      /**
       * @private
       */
      var getSimplex = function getSimplex(initial) {
        var n = initial.length,
          simplex = new Array(n + 1);
        // Initial point to the simplex.
        simplex[0] = initial;
        simplex[0].fx = fn(initial);
        // Create a set of extra points based on the initial.
        for (var i = 0; i < n; ++i) {
          var point = initial.slice();
          point[i] = point[i] ? point[i] * 1.05 : 0.001;
          point.fx = fn(point);
          simplex[i + 1] = point;
        }
        return simplex;
      };
      var updateSimplex = function (simplex, point) {
        point.fx = fn(point);
        simplex[simplex.length - 1] = point;
        return simplex;
      };
      var shrinkSimplex = function (simplex) {
        var best = simplex[0];
        return simplex.map(function (point) {
          var p = weightedSum(1 - pShrink, best, pShrink, point);
          p.fx = fn(p);
          return p;
        });
      };
      var getPoint = function (centroid, worst, a, b) {
        var point = weightedSum(a, centroid, b, worst);
        point.fx = fn(point);
        return point;
      };
      // Create a simplex
      var simplex = getSimplex(initial);
      // Iterate from 0 to max iterations
      for (var i = 0; i < maxIterations; i++) {
        // Sort the simplex
        simplex.sort(sortByFx);
        // Create a centroid from the simplex
        var worst = simplex[simplex.length - 1];
        var centroid = getCentroid(simplex);
        // Calculate the reflected point.
        var reflected = getPoint(centroid, worst, 1 + pRef, -pRef);
        if (reflected.fx < simplex[0].fx) {
          // If reflected point is the best, then possibly expand.
          var expanded = getPoint(centroid, worst, 1 + pExp, -pExp);
          simplex = updateSimplex(
            simplex,
            expanded.fx < reflected.fx ? expanded : reflected
          );
        } else if (reflected.fx >= simplex[simplex.length - 2].fx) {
          // If the reflected point is worse than the second worse, then
          // contract.
          var contracted;
          if (reflected.fx > worst.fx) {
            // If the reflected is worse than the worst point, do a
            // contraction
            contracted = getPoint(centroid, worst, 1 + pCon, -pCon);
            if (contracted.fx < worst.fx) {
              simplex = updateSimplex(simplex, contracted);
            } else {
              simplex = shrinkSimplex(simplex);
            }
          } else {
            // Otherwise do an outwards contraction
            contracted = getPoint(centroid, worst, 1 - pOCon, pOCon);
            if (contracted.fx < reflected.fx) {
              simplex = updateSimplex(simplex, contracted);
            } else {
              simplex = shrinkSimplex(simplex);
            }
          }
        } else {
          simplex = updateSimplex(simplex, reflected);
        }
      }
      return simplex[0];
    };
    var content = {
      getCentroid: getCentroid,
      nelderMead: nelderMead,
    };

    return content;
  });
  _registerModule(
    _modules,
    "modules/venn.src.js",
    [
      _modules["parts/Globals.js"],
      _modules["mixins/draw-point.js"],
      _modules["mixins/geometry.js"],
      _modules["mixins/geometry-circles.js"],
      _modules["mixins/nelder-mead.js"],
      _modules["parts/Utilities.js"],
    ],
    function (H, draw, geometry, GeometryCircleMixin, NelderMeadModule, U) {
      /* *
       *
       *  Experimental Highcharts module which enables visualization of a Venn
       *  diagram.
       *
       *  (c) 2016-2019 Highsoft AS
       *  Authors: Jon Arild Nygard
       *
       *  Layout algorithm by Ben Frederickson:
       *  https://www.benfrederickson.com/better-venn-diagrams/
       *
       *  License: www.highcharts.com/license
       *
       *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
       *
       * */
      var getAreaOfCircle = GeometryCircleMixin.getAreaOfCircle,
        getAreaOfIntersectionBetweenCircles =
          GeometryCircleMixin.getAreaOfIntersectionBetweenCircles,
        getCircleCircleIntersection =
          GeometryCircleMixin.getCircleCircleIntersection,
        getCirclesIntersectionPolygon =
          GeometryCircleMixin.getCirclesIntersectionPolygon,
        getOverlapBetweenCirclesByDistance =
          GeometryCircleMixin.getOverlapBetweenCircles,
        isCircle1CompletelyOverlappingCircle2 =
          GeometryCircleMixin.isCircle1CompletelyOverlappingCircle2,
        isPointInsideAllCircles = GeometryCircleMixin.isPointInsideAllCircles,
        isPointInsideCircle = GeometryCircleMixin.isPointInsideCircle,
        isPointOutsideAllCircles = GeometryCircleMixin.isPointOutsideAllCircles;
      // TODO: replace with individual imports
      var nelderMead = NelderMeadModule.nelderMead;
      var animObject = U.animObject,
        isArray = U.isArray,
        isNumber = U.isNumber,
        isObject = U.isObject,
        isString = U.isString;
      var addEvent = H.addEvent,
        color = H.Color,
        extend = H.extend,
        getCenterOfPoints = geometry.getCenterOfPoints,
        getDistanceBetweenPoints = geometry.getDistanceBetweenPoints,
        merge = H.merge,
        seriesType = H.seriesType,
        seriesTypes = H.seriesTypes;
      var objectValues = function objectValues(obj) {
        return Object.keys(obj).map(function (x) {
          return obj[x];
        });
      };
      /**
       * Calculates the area of overlap between a list of circles.
       * @private
       * @todo add support for calculating overlap between more than 2 circles.
       * @param {Array<Highcharts.CircleObject>} circles
       * List of circles with their given positions.
       * @return {number}
       * Returns the area of overlap between all the circles.
       */
      var getOverlapBetweenCircles = function getOverlapBetweenCircles(
        circles
      ) {
        var overlap = 0;
        // When there is only two circles we can find the overlap by using their
        // radiuses and the distance between them.
        if (circles.length === 2) {
          var circle1 = circles[0];
          var circle2 = circles[1];
          overlap = getOverlapBetweenCirclesByDistance(
            circle1.r,
            circle2.r,
            getDistanceBetweenPoints(circle1, circle2)
          );
        }
        return overlap;
      };
      /**
       * Calculates the difference between the desired overlap and the actual overlap
       * between two circles.
       * @private
       * @param {Dictionary<Highcharts.CircleObject>} mapOfIdToCircle
       * Map from id to circle.
       * @param {Array<Highcharts.VennRelationObject>} relations
       * List of relations to calculate the loss of.
       * @return {number}
       * Returns the loss between positions of the circles for the given relations.
       */
      var loss = function loss(mapOfIdToCircle, relations) {
        var precision = 10e10;
        // Iterate all the relations and calculate their individual loss.
        return relations.reduce(function (totalLoss, relation) {
          var loss = 0;
          if (relation.sets.length > 1) {
            var wantedOverlap = relation.value;
            // Calculate the actual overlap between the sets.
            var actualOverlap = getOverlapBetweenCircles(
              // Get the circles for the given sets.
              relation.sets.map(function (set) {
                return mapOfIdToCircle[set];
              })
            );
            var diff = wantedOverlap - actualOverlap;
            loss = Math.round(diff * diff * precision) / precision;
          }
          // Add calculated loss to the sum.
          return totalLoss + loss;
        }, 0);
      };
      /**
       * Finds the root of a given function. The root is the input value needed for
       * a function to return 0.
       *
       * See https://en.wikipedia.org/wiki/Bisection_method#Algorithm
       *
       * TODO: Add unit tests.
       *
       * @param {Function} f
       * The function to find the root of.
       * @param {number} a
       * The lowest number in the search range.
       * @param {number} b
       * The highest number in the search range.
       * @param {number} [tolerance=1e-10]
       * The allowed difference between the returned value and root.
       * @param {number} [maxIterations=100]
       * The maximum iterations allowed.
       * @return {number}
       * Root number.
       */
      var bisect = function bisect(f, a, b, tolerance, maxIterations) {
        var fA = f(a),
          fB = f(b),
          nMax = maxIterations || 100,
          tol = tolerance || 1e-10,
          delta = b - a,
          n = 1,
          x,
          fX;
        if (a >= b) {
          throw new Error("a must be smaller than b.");
        } else if (fA * fB > 0) {
          throw new Error("f(a) and f(b) must have opposite signs.");
        }
        if (fA === 0) {
          x = a;
        } else if (fB === 0) {
          x = b;
        } else {
          while (n++ <= nMax && fX !== 0 && delta > tol) {
            delta = (b - a) / 2;
            x = a + delta;
            fX = f(x);
            // Update low and high for next search interval.
            if (fA * fX > 0) {
              a = x;
            } else {
              b = x;
            }
          }
        }
        return x;
      };
      /**
       * Uses the bisection method to make a best guess of the ideal distance between
       * two circles too get the desired overlap.
       * Currently there is no known formula to calculate the distance from the area
       * of overlap, which makes the bisection method preferred.
       * @private
       * @param {number} r1
       * Radius of the first circle.
       * @param {number} r2
       * Radiues of the second circle.
       * @param {number} overlap
       * The wanted overlap between the two circles.
       * @return {number}
       * Returns the distance needed to get the wanted overlap between the two
       * circles.
       */
      var getDistanceBetweenCirclesByOverlap =
        function getDistanceBetweenCirclesByOverlap(r1, r2, overlap) {
          var maxDistance = r1 + r2,
            distance;
          if (overlap <= 0) {
            // If overlap is below or equal to zero, then there is no overlap.
            distance = maxDistance;
          } else if (getAreaOfCircle(r1 < r2 ? r1 : r2) <= overlap) {
            // When area of overlap is larger than the area of the smallest circle,
            // then it is completely overlapping.
            distance = 0;
          } else {
            distance = bisect(
              function (x) {
                var actualOverlap = getOverlapBetweenCirclesByDistance(
                  r1,
                  r2,
                  x
                );
                // Return the differance between wanted and actual overlap.
                return overlap - actualOverlap;
              },
              0,
              maxDistance
            );
          }
          return distance;
        };
      var isSet = function (x) {
        return isArray(x.sets) && x.sets.length === 1;
      };
      /**
       * Calculates a margin for a point based on the iternal and external circles.
       * The margin describes if the point is well placed within the internal circles,
       * and away from the external
       * @private
       * @todo add unit tests.
       * @param {Highcharts.PositionObject} point
       * The point to evaluate.
       * @param {Array<Highcharts.CircleObject>} internal
       * The internal circles.
       * @param {Array<Highcharts.CircleObject>} external
       * The external circles.
       * @return {number}
       * Returns the margin.
       */
      var getMarginFromCircles = function getMarginFromCircles(
        point,
        internal,
        external
      ) {
        var margin = internal.reduce(function (margin, circle) {
          var m = circle.r - getDistanceBetweenPoints(point, circle);
          return m <= margin ? m : margin;
        }, Number.MAX_VALUE);
        margin = external.reduce(function (margin, circle) {
          var m = getDistanceBetweenPoints(point, circle) - circle.r;
          return m <= margin ? m : margin;
        }, margin);
        return margin;
      };
      /**
       * Finds the optimal label position by looking for a position that has a low
       * distance from the internal circles, and as large possible distane to the
       * external circles.
       * @private
       * @todo Optimize the intial position.
       * @todo Add unit tests.
       * @param {Array<Highcharts.CircleObject>} internal
       * Internal circles.
       * @param {Array<Highcharts.CircleObject>} external
       * External circles.
       * @return {Highcharts.PositionObject}
       * Returns the found position.
       */
      var getLabelPosition = function getLabelPosition(internal, external) {
        // Get the best label position within the internal circles.
        var best = internal.reduce(
          function (best, circle) {
            var d = circle.r / 2;
            // Give a set of points with the circle to evaluate as the best label
            // position.
            return (
              [
                { x: circle.x, y: circle.y },
                { x: circle.x + d, y: circle.y },
                { x: circle.x - d, y: circle.y },
                { x: circle.x, y: circle.y + d },
                { x: circle.x, y: circle.y - d },
              ]
                // Iterate the given points and return the one with the largest
                // margin.
                .reduce(function (best, point) {
                  var margin = getMarginFromCircles(point, internal, external);
                  // If the margin better than the current best, then update best.
                  if (best.margin < margin) {
                    best.point = point;
                    best.margin = margin;
                  }
                  return best;
                }, best)
            );
          },
          {
            point: void 0,
            margin: -Number.MAX_VALUE,
          }
        ).point;
        // Use nelder mead to optimize the initial label position.
        var optimal = nelderMead(
          function (p) {
            return -getMarginFromCircles(
              { x: p[0], y: p[1] },
              internal,
              external
            );
          },
          [best.x, best.y]
        );
        // Update best to be the point which was found to have the best margin.
        best = {
          x: optimal[0],
          y: optimal[1],
        };
        if (
          !(
            isPointInsideAllCircles(best, internal) &&
            isPointOutsideAllCircles(best, external)
          )
        ) {
          // If point was either outside one of the internal, or inside one of the
          // external, then it was invalid and should use a fallback.
          if (internal.length > 1) {
            best = getCenterOfPoints(getCirclesIntersectionPolygon(internal));
          } else {
            best = {
              x: internal[0].x,
              y: internal[0].y,
            };
          }
        }
        // Return the best point.
        return best;
      };
      /**
       * Finds the available width for a label, by taking the label position and
       * finding the largest distance, which is inside all internal circles, and
       * outside all external circles.
       *
       * @private
       * @param {Highcharts.PositionObject} pos
       * The x and y coordinate of the label.
       * @param {Array<Highcharts.CircleObject>} internal
       * Internal circles.
       * @param {Array<Highcharts.CircleObject>} external
       * External circles.
       * @return {number}
       * Returns available width for the label.
       */
      var getLabelWidth = function getLabelWidth(pos, internal, external) {
        var radius = internal.reduce(function (min, circle) {
            return Math.min(circle.r, min);
          }, Infinity),
          // Filter out external circles that are completely overlapping.
          filteredExternals = external.filter(function (circle) {
            return !isPointInsideCircle(pos, circle);
          });
        var findDistance = function (maxDistance, direction) {
          return bisect(
            function (x) {
              var testPos = {
                  x: pos.x + direction * x,
                  y: pos.y,
                },
                isValid =
                  isPointInsideAllCircles(testPos, internal) &&
                  isPointOutsideAllCircles(testPos, filteredExternals);
              // If the position is valid, then we want to move towards the max
              // distance. If not, then we want to  away from the max distance.
              return -(maxDistance - x) + (isValid ? 0 : Number.MAX_VALUE);
            },
            0,
            maxDistance
          );
        };
        // Find the smallest distance of left and right.
        return Math.min(findDistance(radius, -1), findDistance(radius, 1)) * 2;
      };
      /**
       * Calulates data label values for a given relations object.
       *
       * @private
       * @todo add unit tests
       * @param {Highcharts.VennRelationObject} relation A relations object.
       * @param {Array<Highcharts.VennRelationObject>} setRelations The list of
       * relations that is a set.
       * @return {Highcharts.VennLabelValuesObject}
       * Returns an object containing position and width of the label.
       */
      function getLabelValues(relation, setRelations) {
        var sets = relation.sets;
        // Create a list of internal and external circles.
        var data = setRelations.reduce(
          function (data, set) {
            // If the set exists in this relation, then it is internal,
            // otherwise it will be external.
            var isInternal = sets.indexOf(set.sets[0]) > -1;
            var property = isInternal ? "internal" : "external";
            // Add the circle to the list.
            data[property].push(set.circle);
            return data;
          },
          {
            internal: [],
            external: [],
          }
        );
        // Filter out external circles that are completely overlapping all internal
        data.external = data.external.filter(function (externalCircle) {
          return data.internal.some(function (internalCircle) {
            return !isCircle1CompletelyOverlappingCircle2(
              externalCircle,
              internalCircle
            );
          });
        });
        // Calulate the label position.
        var position = getLabelPosition(data.internal, data.external);
        // Calculate the label width
        var width = getLabelWidth(position, data.internal, data.external);
        return {
          position: position,
          width: width,
        };
      }
      /**
       * Takes an array of relations and adds the properties `totalOverlap` and
       * `overlapping` to each set. The property `totalOverlap` is the sum of value
       * for each relation where this set is included. The property `overlapping` is
       * a map of how much this set is overlapping another set.
       * NOTE: This algorithm ignores relations consisting of more than 2 sets.
       * @private
       * @param {Array<Highcharts.VennRelationObject>} relations
       * The list of relations that should be sorted.
       * @return {Array<Highcharts.VennRelationObject>}
       * Returns the modified input relations with added properties `totalOverlap` and
       * `overlapping`.
       */
      var addOverlapToSets = function addOverlapToSets(relations) {
        // Calculate the amount of overlap per set.
        var mapOfIdToProps = relations
          // Filter out relations consisting of 2 sets.
          .filter(function (relation) {
            return relation.sets.length === 2;
          })
          // Sum up the amount of overlap for each set.
          .reduce(function (map, relation) {
            var sets = relation.sets;
            sets.forEach(function (set, i, arr) {
              if (!isObject(map[set])) {
                map[set] = {
                  overlapping: {},
                  totalOverlap: 0,
                };
              }
              map[set].totalOverlap += relation.value;
              map[set].overlapping[arr[1 - i]] = relation.value;
            });
            return map;
          }, {});
        relations
          // Filter out single sets
          .filter(isSet)
          // Extend the set with the calculated properties.
          .forEach(function (set) {
            var properties = mapOfIdToProps[set.sets[0]];
            extend(set, properties);
          });
        // Returns the modified relations.
        return relations;
      };
      /**
       * Takes two sets and finds the one with the largest total overlap.
       * @private
       * @param {object} a The first set to compare.
       * @param {object} b The second set to compare.
       * @return {number} Returns 0 if a and b are equal, <0 if a is greater, >0 if b
       * is greater.
       */
      var sortByTotalOverlap = function sortByTotalOverlap(a, b) {
        return b.totalOverlap - a.totalOverlap;
      };
      /**
       * Uses a greedy approach to position all the sets. Works well with a small
       * number of sets, and are in these cases a good choice aesthetically.
       * @private
       * @param {Array<object>} relations List of the overlap between two or more
       * sets, or the size of a single set.
       * @return {Array<object>} List of circles and their calculated positions.
       */
      var layoutGreedyVenn = function layoutGreedyVenn(relations) {
        var positionedSets = [],
          mapOfIdToCircles = {};
        // Define a circle for each set.
        relations
          .filter(function (relation) {
            return relation.sets.length === 1;
          })
          .forEach(function (relation) {
            mapOfIdToCircles[relation.sets[0]] = relation.circle = {
              x: Number.MAX_VALUE,
              y: Number.MAX_VALUE,
              r: Math.sqrt(relation.value / Math.PI),
            };
          });
        /**
         * Takes a set and updates the position, and add the set to the list of
         * positioned sets.
         * @private
         * @param {object} set
         * The set to add to its final position.
         * @param {object} coordinates
         * The coordinates to position the set at.
         * @return {void}
         */
        var positionSet = function positionSet(set, coordinates) {
          var circle = set.circle;
          circle.x = coordinates.x;
          circle.y = coordinates.y;
          positionedSets.push(set);
        };
        // Find overlap between sets. Ignore relations with more then 2 sets.
        addOverlapToSets(relations);
        // Sort sets by the sum of their size from large to small.
        var sortedByOverlap = relations.filter(isSet).sort(sortByTotalOverlap);
        // Position the most overlapped set at 0,0.
        positionSet(sortedByOverlap.shift(), { x: 0, y: 0 });
        var relationsWithTwoSets = relations.filter(function (x) {
          return x.sets.length === 2;
        });
        // Iterate and position the remaining sets.
        sortedByOverlap.forEach(function (set) {
          var circle = set.circle,
            radius = circle.r,
            overlapping = set.overlapping;
          var bestPosition = positionedSets.reduce(
            function (best, positionedSet, i) {
              var positionedCircle = positionedSet.circle,
                overlap = overlapping[positionedSet.sets[0]];
              // Calculate the distance between the sets to get the correct
              // overlap
              var distance = getDistanceBetweenCirclesByOverlap(
                radius,
                positionedCircle.r,
                overlap
              );
              // Create a list of possible coordinates calculated from
              // distance.
              var possibleCoordinates = [
                { x: positionedCircle.x + distance, y: positionedCircle.y },
                { x: positionedCircle.x - distance, y: positionedCircle.y },
                { x: positionedCircle.x, y: positionedCircle.y + distance },
                { x: positionedCircle.x, y: positionedCircle.y - distance },
              ];
              // If there are more circles overlapping, then add the
              // intersection points as possible positions.
              positionedSets.slice(i + 1).forEach(function (positionedSet2) {
                var positionedCircle2 = positionedSet2.circle,
                  overlap2 = overlapping[positionedSet2.sets[0]],
                  distance2 = getDistanceBetweenCirclesByOverlap(
                    radius,
                    positionedCircle2.r,
                    overlap2
                  );
                // Add intersections to list of coordinates.
                possibleCoordinates = possibleCoordinates.concat(
                  getCircleCircleIntersection(
                    {
                      x: positionedCircle.x,
                      y: positionedCircle.y,
                      r: distance,
                    },
                    {
                      x: positionedCircle2.x,
                      y: positionedCircle2.y,
                      r: distance2,
                    }
                  )
                );
              });
              // Iterate all suggested coordinates and find the best one.
              possibleCoordinates.forEach(function (coordinates) {
                circle.x = coordinates.x;
                circle.y = coordinates.y;
                // Calculate loss for the suggested coordinates.
                var currentLoss = loss(mapOfIdToCircles, relationsWithTwoSets);
                // If the loss is better, then use these new coordinates.
                if (currentLoss < best.loss) {
                  best.loss = currentLoss;
                  best.coordinates = coordinates;
                }
              });
              // Return resulting coordinates.
              return best;
            },
            {
              loss: Number.MAX_VALUE,
              coordinates: void 0,
            }
          );
          // Add the set to its final position.
          positionSet(set, bestPosition.coordinates);
        });
        // Return the positions of each set.
        return mapOfIdToCircles;
      };
      /**
       * Calculates the positions, and the label values of all the sets in the venn
       * diagram.
       *
       * @private
       * @todo Add support for constrained MDS.
       * @param {Array<Highchats.VennRelationObject>} relations
       * List of the overlap between two or more sets, or the size of a single set.
       * @return {Highcharts.Dictionary<*>}
       * List of circles and their calculated positions.
       */
      function layout(relations) {
        var mapOfIdToShape = {};
        var mapOfIdToLabelValues = {};
        // Calculate best initial positions by using greedy layout.
        if (relations.length > 0) {
          var mapOfIdToCircles_1 = layoutGreedyVenn(relations);
          var setRelations_1 = relations.filter(isSet);
          relations.forEach(function (relation) {
            var sets = relation.sets;
            var id = sets.join();
            // Get shape from map of circles, or calculate intersection.
            var shape = isSet(relation)
              ? mapOfIdToCircles_1[id]
              : getAreaOfIntersectionBetweenCircles(
                  sets.map(function (set) {
                    return mapOfIdToCircles_1[set];
                  })
                );
            // Calculate label values if the set has a shape
            if (shape) {
              mapOfIdToShape[id] = shape;
              mapOfIdToLabelValues[id] = getLabelValues(
                relation,
                setRelations_1
              );
            }
          });
        }
        return {
          mapOfIdToShape: mapOfIdToShape,
          mapOfIdToLabelValues: mapOfIdToLabelValues,
        };
      }
      var isValidRelation = function (x) {
        var map = {};
        return (
          isObject(x) &&
          isNumber(x.value) &&
          x.value > -1 &&
          isArray(x.sets) &&
          x.sets.length > 0 &&
          !x.sets.some(function (set) {
            var invalid = false;
            if (!map[set] && isString(set)) {
              map[set] = true;
            } else {
              invalid = true;
            }
            return invalid;
          })
        );
      };
      var isValidSet = function (x) {
        return isValidRelation(x) && isSet(x) && x.value > 0;
      };
      /**
       * Prepares the venn data so that it is usable for the layout function. Filter
       * out sets, or intersections that includes sets, that are missing in the data
       * or has (value < 1). Adds missing relations between sets in the data as
       * value = 0.
       * @private
       * @param {Array<object>} data The raw input data.
       * @return {Array<object>} Returns an array of valid venn data.
       */
      var processVennData = function processVennData(data) {
        var d = isArray(data) ? data : [];
        var validSets = d
          .reduce(function (arr, x) {
            // Check if x is a valid set, and that it is not an duplicate.
            if (isValidSet(x) && arr.indexOf(x.sets[0]) === -1) {
              arr.push(x.sets[0]);
            }
            return arr;
          }, [])
          .sort();
        var mapOfIdToRelation = d.reduce(function (
          mapOfIdToRelation,
          relation
        ) {
          if (
            isValidRelation(relation) &&
            !relation.sets.some(function (set) {
              return validSets.indexOf(set) === -1;
            })
          ) {
            mapOfIdToRelation[relation.sets.sort().join()] = relation;
          }
          return mapOfIdToRelation;
        },
        {});
        validSets
          .reduce(function (combinations, set, i, arr) {
            var remaining = arr.slice(i + 1);
            remaining.forEach(function (set2) {
              combinations.push(set + "," + set2);
            });
            return combinations;
          }, [])
          .forEach(function (combination) {
            if (!mapOfIdToRelation[combination]) {
              var obj = {
                sets: combination.split(","),
                value: 0,
              };
              mapOfIdToRelation[combination] = obj;
            }
          });
        // Transform map into array.
        return objectValues(mapOfIdToRelation);
      };
      /**
       * Calculates the proper scale to fit the cloud inside the plotting area.
       * @private
       * @todo add unit test
       * @param {number} targetWidth
       * Width of target area.
       * @param {number} targetHeight
       * Height of target area.
       * @param {Highcharts.PolygonBoxObject} field
       * The playing field.
       * @return {Highcharts.Dictionary<number>}
       * Returns the value to scale the playing field up to the size of the target
       * area, and center of x and y.
       */
      var getScale = function getScale(targetWidth, targetHeight, field) {
        var height = field.bottom - field.top, // top is smaller than bottom
          width = field.right - field.left,
          scaleX = width > 0 ? (1 / width) * targetWidth : 1,
          scaleY = height > 0 ? (1 / height) * targetHeight : 1,
          adjustX = (field.right + field.left) / 2,
          adjustY = (field.top + field.bottom) / 2,
          scale = Math.min(scaleX, scaleY);
        return {
          scale: scale,
          centerX: targetWidth / 2 - adjustX * scale,
          centerY: targetHeight / 2 - adjustY * scale,
        };
      };
      /**
       * If a circle is outside a give field, then the boundaries of the field is
       * adjusted accordingly. Modifies the field object which is passed as the first
       * parameter.
       * @private
       * @todo NOTE: Copied from wordcloud, can probably be unified.
       * @param {Highcharts.PolygonBoxObject} field
       * The bounding box of a playing field.
       * @param {Highcharts.CircleObject} circle
       * The bounding box for a placed point.
       * @return {Highcharts.PolygonBoxObject}
       * Returns a modified field object.
       */
      var updateFieldBoundaries = function updateFieldBoundaries(
        field,
        circle
      ) {
        var left = circle.x - circle.r,
          right = circle.x + circle.r,
          bottom = circle.y + circle.r,
          top = circle.y - circle.r;
        // TODO improve type checking.
        if (!isNumber(field.left) || field.left > left) {
          field.left = left;
        }
        if (!isNumber(field.right) || field.right < right) {
          field.right = right;
        }
        if (!isNumber(field.top) || field.top > top) {
          field.top = top;
        }
        if (!isNumber(field.bottom) || field.bottom < bottom) {
          field.bottom = bottom;
        }
        return field;
      };
      /**
       * A Venn diagram displays all possible logical relations between a collection
       * of different sets. The sets are represented by circles, and the relation
       * between the sets are displayed by the overlap or lack of overlap between
       * them. The venn diagram is a special case of Euler diagrams, which can also
       * be displayed by this series type.
       *
       * @sample {highcharts} highcharts/demo/venn-diagram/
       *         Venn diagram
       * @sample {highcharts} highcharts/demo/euler-diagram/
       *         Euler diagram
       *
       * @extends      plotOptions.scatter
       * @excluding    connectEnds, connectNulls, cropThreshold, dragDrop,
       *               findNearestPointBy, getExtremesFromAll, jitter, label, linecap,
       *               lineWidth, linkedTo, marker, negativeColor, pointInterval,
       *               pointIntervalUnit, pointPlacement, pointStart, softThreshold,
       *               stacking, steps, threshold, xAxis, yAxis, zoneAxis, zones
       * @product      highcharts
       * @requires     modules/venn
       * @optionparent plotOptions.venn
       */
      var vennOptions = {
        borderColor: "#cccccc",
        borderDashStyle: "solid",
        borderWidth: 1,
        brighten: 0,
        clip: false,
        colorByPoint: true,
        dataLabels: {
          enabled: true,
          verticalAlign: "middle",
          formatter: function () {
            return this.point.name;
          },
        },
        /**
         * @ignore-option
         * @private
         */
        inactiveOtherPoints: true,
        marker: false,
        opacity: 0.75,
        showInLegend: false,
        states: {
          /**
           * @excluding halo
           */
          hover: {
            opacity: 1,
            borderColor: "#333333",
          },
          /**
           * @excluding halo
           */
          select: {
            color: "#cccccc",
            borderColor: "#000000",
            animation: false,
          },
        },
        tooltip: {
          pointFormat: "{point.name}: {point.value}",
        },
      };
      var vennSeries = {
        isCartesian: false,
        axisTypes: [],
        directTouch: true,
        pointArrayMap: ["value"],
        translate: function () {
          var chart = this.chart;
          this.processedXData = this.xData;
          this.generatePoints();
          // Process the data before passing it into the layout function.
          var relations = processVennData(this.options.data);
          // Calculate the positions of each circle.
          var _a = layout(relations),
            mapOfIdToShape = _a.mapOfIdToShape,
            mapOfIdToLabelValues = _a.mapOfIdToLabelValues;
          // Calculate the scale, and center of the plot area.
          var field = Object.keys(mapOfIdToShape)
              .filter(function (key) {
                var shape = mapOfIdToShape[key];
                return shape && isNumber(shape.r);
              })
              .reduce(
                function (field, key) {
                  return updateFieldBoundaries(field, mapOfIdToShape[key]);
                },
                { top: 0, bottom: 0, left: 0, right: 0 }
              ),
            scaling = getScale(chart.plotWidth, chart.plotHeight, field),
            scale = scaling.scale,
            centerX = scaling.centerX,
            centerY = scaling.centerY;
          // Iterate all points and calculate and draw their graphics.
          this.points.forEach(function (point) {
            var sets = isArray(point.sets) ? point.sets : [],
              id = sets.join(),
              shape = mapOfIdToShape[id],
              shapeArgs,
              dataLabelValues = mapOfIdToLabelValues[id] || {},
              dataLabelWidth = dataLabelValues.width,
              dataLabelPosition = dataLabelValues.position,
              dlOptions = point.options && point.options.dataLabels;
            if (shape) {
              if (shape.r) {
                shapeArgs = {
                  x: centerX + shape.x * scale,
                  y: centerY + shape.y * scale,
                  r: shape.r * scale,
                };
              } else if (shape.d) {
                // TODO: find a better way to handle scaling of a path.
                var d = shape.d
                  .reduce(function (path, arr) {
                    if (arr[0] === "M") {
                      arr[1] = centerX + arr[1] * scale;
                      arr[2] = centerY + arr[2] * scale;
                    } else if (arr[0] === "A") {
                      arr[1] = arr[1] * scale;
                      arr[2] = arr[2] * scale;
                      arr[6] = centerX + arr[6] * scale;
                      arr[7] = centerY + arr[7] * scale;
                    }
                    return path.concat(arr);
                  }, [])
                  .join(" ");
                shapeArgs = {
                  d: d,
                };
              }
              // Scale the position for the data label.
              if (dataLabelPosition) {
                dataLabelPosition.x = centerX + dataLabelPosition.x * scale;
                dataLabelPosition.y = centerY + dataLabelPosition.y * scale;
              } else {
                dataLabelPosition = {};
              }
              if (isNumber(dataLabelWidth)) {
                dataLabelWidth = Math.round(dataLabelWidth * scale);
              }
            }
            point.shapeArgs = shapeArgs;
            // Placement for the data labels
            if (dataLabelPosition && shapeArgs) {
              point.plotX = dataLabelPosition.x;
              point.plotY = dataLabelPosition.y;
            }
            // Add width for the data label
            if (dataLabelWidth && shapeArgs) {
              point.dlOptions = merge(
                true,
                {
                  style: {
                    width: dataLabelWidth,
                  },
                },
                isObject(dlOptions) && dlOptions
              );
            }
            // Set name for usage in tooltip and in data label.
            point.name = point.options.name || sets.join("∩");
          });
        },
        /* eslint-disable valid-jsdoc */
        /**
         * Draw the graphics for each point.
         * @private
         */
        drawPoints: function () {
          var series = this,
            // Series properties
            chart = series.chart,
            group = series.group,
            points = series.points || [],
            // Chart properties
            renderer = chart.renderer;
          // Iterate all points and calculate and draw their graphics.
          points.forEach(function (point) {
            var attribs = {
                zIndex: isArray(point.sets) ? point.sets.length : 0,
              },
              shapeArgs = point.shapeArgs;
            // Add point attribs
            if (!chart.styledMode) {
              extend(attribs, series.pointAttribs(point, point.state));
            }
            // Draw the point graphic.
            point.draw({
              isNew: !point.graphic,
              animatableAttribs: shapeArgs,
              attribs: attribs,
              group: group,
              renderer: renderer,
              shapeType: shapeArgs && shapeArgs.d ? "path" : "circle",
            });
          });
        },
        /**
         * Calculates the style attributes for a point. The attributes can vary
         * depending on the state of the point.
         * @private
         * @param {Highcharts.Point} point
         * The point which will get the resulting attributes.
         * @param {string} [state]
         * The state of the point.
         * @return {Highcharts.SVGAttributes}
         * Returns the calculated attributes.
         */
        pointAttribs: function (point, state) {
          var series = this,
            seriesOptions = series.options || {},
            pointOptions = (point && point.options) || {},
            stateOptions = (state && seriesOptions.states[state]) || {},
            options = merge(
              seriesOptions,
              { color: point && point.color },
              pointOptions,
              stateOptions
            );
          // Return resulting values for the attributes.
          return {
            fill: color(options.color)
              .setOpacity(options.opacity)
              .brighten(options.brightness)
              .get(),
            stroke: options.borderColor,
            "stroke-width": options.borderWidth,
            dashstyle: options.borderDashStyle,
          };
        },
        /* eslint-enable valid-jsdoc */
        animate: function (init) {
          if (!init) {
            var series = this,
              animOptions = animObject(series.options.animation);
            series.points.forEach(function (point) {
              var args = point.shapeArgs;
              if (point.graphic && args) {
                var attr = {},
                  animate = {};
                if (args.d) {
                  // If shape is a path, then animate opacity.
                  attr.opacity = 0.001;
                } else {
                  // If shape is a circle, then animate radius.
                  attr.r = 0;
                  animate.r = args.r;
                }
                point.graphic.attr(attr).animate(animate, animOptions);
                // If shape is path, then fade it in after the circles
                // animation
                if (args.d) {
                  setTimeout(function () {
                    if (point && point.graphic) {
                      point.graphic.animate({
                        opacity: 1,
                      });
                    }
                  }, animOptions.duration);
                }
              }
            }, series);
            series.animate = null;
          }
        },
        utils: {
          addOverlapToSets: addOverlapToSets,
          geometry: geometry,
          geometryCircles: GeometryCircleMixin,
          getLabelWidth: getLabelWidth,
          getMarginFromCircles: getMarginFromCircles,
          getDistanceBetweenCirclesByOverlap:
            getDistanceBetweenCirclesByOverlap,
          layoutGreedyVenn: layoutGreedyVenn,
          loss: loss,
          nelderMead: NelderMeadModule,
          processVennData: processVennData,
          sortByTotalOverlap: sortByTotalOverlap,
        },
      };
      var vennPoint = {
        draw: draw,
        shouldDraw: function () {
          var point = this;
          // Only draw points with single sets.
          return !!point.shapeArgs;
        },
        isValid: function () {
          return isNumber(this.value);
        },
      };
      /**
       * A `venn` series. If the [type](#series.venn.type) option is
       * not specified, it is inherited from [chart.type](#chart.type).
       *
       * @extends   series,plotOptions.venn
       * @excluding connectEnds, connectNulls, cropThreshold, dataParser, dataURL,
       *            findNearestPointBy, getExtremesFromAll, label, linecap, lineWidth,
       *            linkedTo, marker, negativeColor, pointInterval, pointIntervalUnit,
       *            pointPlacement, pointStart, softThreshold, stack, stacking, steps,
       *            threshold, xAxis, yAxis, zoneAxis, zones
       * @product   highcharts
       * @requires  modules/venn
       * @apioption series.venn
       */
      /**
       * @type      {Array<*>}
       * @extends   series.scatter.data
       * @excluding marker, x, y
       * @product   highcharts
       * @apioption series.venn.data
       */
      /**
       * The name of the point. Used in data labels and tooltip. If name is not
       * defined then it will default to the joined values in
       * [sets](#series.venn.sets).
       *
       * @sample {highcharts} highcharts/demo/venn-diagram/
       *         Venn diagram
       * @sample {highcharts} highcharts/demo/euler-diagram/
       *         Euler diagram
       *
       * @type      {number}
       * @since     7.0.0
       * @product   highcharts
       * @apioption series.venn.data.name
       */
      /**
       * The value of the point, resulting in a relative area of the circle, or area
       * of overlap between two sets in the venn or euler diagram.
       *
       * @sample {highcharts} highcharts/demo/venn-diagram/
       *         Venn diagram
       * @sample {highcharts} highcharts/demo/euler-diagram/
       *         Euler diagram
       *
       * @type      {number}
       * @since     7.0.0
       * @product   highcharts
       * @apioption series.venn.data.value
       */
      /**
       * The set or sets the options will be applied to. If a single entry is defined,
       * then it will create a new set. If more than one entry is defined, then it
       * will define the overlap between the sets in the array.
       *
       * @sample {highcharts} highcharts/demo/venn-diagram/
       *         Venn diagram
       * @sample {highcharts} highcharts/demo/euler-diagram/
       *         Euler diagram
       *
       * @type      {Array<string>}
       * @since     7.0.0
       * @product   highcharts
       * @apioption series.venn.data.sets
       */
      /**
       * @excluding halo
       * @apioption series.venn.states.hover
       */
      /**
       * @excluding halo
       * @apioption series.venn.states.select
       */
      /**
       * @private
       * @class
       * @name Highcharts.seriesTypes.venn
       *
       * @augments Highcharts.Series
       */
      seriesType("venn", "scatter", vennOptions, vennSeries, vennPoint);
      /* eslint-disable no-invalid-this */
      // Modify final series options.
      addEvent(seriesTypes.venn, "afterSetOptions", function (e) {
        var options = e.options,
          states = options.states;
        if (this instanceof seriesTypes.venn) {
          // Explicitly disable all halo options.
          Object.keys(states).forEach(function (state) {
            states[state].halo = false;
          });
        }
      });
    }
  );
  _registerModule(_modules, "masters/modules/venn.src.js", [], function () {});
});
